When the set \(\Theta _{0}\)  is a singleton,
the derivative map \(\phi _{f}^{\prime }\)  in (REF ) is identically zero
and the corresponding limiting distribution \(L\)  is degenerate.
To obtain an informative limiting distribution in this case,
our approach would need to be modified.
One possibility is to apply a higher-order functional delta method
based on second-order directional derivatives
similarly as in the second-order analysis for minimization problems
in [1]}.
However, we do not pursue this further as
in the case of a single solution confidence sets can be directly formed based on the
asymptotic normality result of [2]}.
